Towards the Unified Theory of Galactic Bar-Modes

The arguments in favor of the unified formation mechanism for both slow (Lynden-Bell’s) bars and common fast bars are given. This mechanism consists in a certain instability that is akin to the well-known radial orbit instability; it is caused by the mutual attraction and alignment of axes of precessing star orbits (up to now, such a way of formation was considered only for slow bars). The general theory of the low-frequency modes of a disk consisting of precessing orbits (at different angular velocities) is presented. The problem of determining these modes is reduced to the integral equations of a rather simple structure. The characteristic pattern speeds (Ω p ) of the low-frequency modes are of order of the mean orbit precession speeds (¯Ω pr ). The bar-modes also belong to this type of modes. The slow bars have Ω p ≈ ¯Ω pr ; for the fast bars, Ω p may far exceed even the maximum precessing speed of disk orbits (however, Ω p remains to be of order of these precessing speeds). The possibility of such an excess of Ω p over Ω max pr is connected with the effect of “repelling” orbits that tend to move in the direction opposite to that they are being pushed. The preliminary analysis of the orbit precession patterns for a number of typical potentials is given. It is noted that the maximum radius of the “attracting” circular orbits ( r c ) may be used as a reasonable estimate of a bar length.